45 research outputs found
Tools for calculations in color space
Both the higher energy and the initial state colored partons contribute to
making exact calculations in QCD color space more important at the LHC than at
its predecessors. This is applicable whether the method of assessing QCD is
fixed order calculation, resummation, or parton showers. In this talk we
discuss tools for tackling the problem of performing exact color summed
calculations. We start with theoretical tools in the form of the (standard)
trace bases and the orthogonal multiplet bases (for which a general method of
construction was recently presented). Following this, we focus on two new
packages for performing color structure calculations: one easy to use
Mathematica package, ColorMath, and one C++ package, ColorFull, which is
suitable for more demanding calculations, and for interfacing with event
generators.Comment: 7 pages, to appear in the proceedings of the XXI International
Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2013), 22-26
April 2013, Marseilles, Franc
Orthogonal multiplet bases in SU(Nc) color space
We develop a general recipe for constructing orthogonal bases for the
calculation of color structures appearing in QCD for any number of partons and
arbitrary Nc. The bases are constructed using hermitian gluon projectors onto
irreducible subspaces invariant under SU(Nc). Thus, each basis vector is
associated with an irreducible representation of SU(Nc). The resulting
multiplet bases are not only orthogonal, but also minimal for finite Nc. As a
consequence, for calculations involving many colored particles, the number of
basis vectors is reduced significantly compared to standard approaches
employing overcomplete bases. We exemplify the method by constructing multiplet
bases for all processes involving a total of 6 external colored partons.Comment: 50 pages, 2 figure
Semiclassical quantisation rules for the Dirac and Pauli equations
We derive explicit semiclassical quantisation conditions for the Dirac and
Pauli equations. We show that the spin degree of freedom yields a contribution
which is of the same order of magnitude as the Maslov correction in
Einstein-Brillouin-Keller quantisation. In order to obtain this result a
generalisation of the notion of integrability for a certain skew product flow
of classical translational dynamics and classical spin precession has to be
derived. Among the examples discussed is the relativistic Kepler problem with
Thomas precession, whose treatment sheds some light on the amazing success of
Sommerfeld's theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1--91].Comment: 36 pages, 2 figure
Polyakov loops and SU(2) staggered Dirac spectra
We consider the spectrum of the staggered Dirac operator with SU(2) gauge
fields. Our study is motivated by the fact that the antiunitary symmetries of
this operator are different from those of the SU(2) continuum Dirac operator.
In this contribution, we investigate in some detail staggered eigenvalue
spectra close to the free limit. Numerical experiments in the quenched
approximation and at very large -values show that the eigenvalues occur
in clusters consisting of eight eigenvalues each. We can predict the locations
of these clusters for a given configuration very accurately by an analytical
formula involving Polyakov loops and boundary conditions. The spacing
distribution of the eigenvalues within the clusters agrees with the chiral
symplectic ensemble of random matrix theory, in agreement with theoretical
expectations, whereas the spacing distribution between the clusters tends
towards Poisson behavior.Comment: 7 pages, 4 figures, talk given by M. Panero at the XXV International
Symposium on Lattice Field Theory, Regensburg, Germany, 30 July - 4 August
200
Particle creation and annihilation at interior boundaries:One-dimensional models
We describe creation and annihilation of particles at external sources in one
spatial dimension in terms of interior-boundary conditions (IBCs). We derive
explicit solutions for spectra, (generalised) eigenfunctions, as well as Green
functions, spectral determinants, and integrated spectral densities. Moreover,
we introduce a quantum graph version of IBC-Hamiltonians.Comment: 32 page
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The Berry-Keating operator on a lattice
We construct and study a version of the Berry-Keating operator with a built-in
truncation of the phase space, which we choose to be a two-dimensional torus. The
operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic
oscillator, producing a difference operator on a finite, periodic lattice. We investigate
the continuum and the infinite-volume limit of our model in conjunction with the
semiclassical limit. Using semiclassical methods, we show that a specific combination
of the limits leads to a logarithmic mean spectral density as it was anticipated by
Berry and Keating
The Berry-Keating operator on a lattice
We construct and study a version of the Berry-Keating operator with a
built-in truncation of the phase space, which we choose to be a two-dimensional
torus. The operator is a Weyl quantisation of the classical Hamiltonian for an
inverted harmonic oscillator, producing a difference operator on a finite,
periodic lattice. We investigate the continuum and the infinite-volume limit of
our model in conjunction with the semiclassical limit. Using semiclassical
methods, we show that a specific combination of the limits leads to a
logarithmic mean spectral density as it was anticipated by Berry and Keating